is the average annual **coupon rate** based on a $100 price assumptions? I assumed the coupon YIELD is based on the beginning year bond price already and thus no need for adjustment. Seems that the answer here sees it different. The examples in the books all have beginning bond prices at $100 which is not helpful…

Exhibit 3

Selected Information for Calculation of Expected Return for Portfolio C

Investment horizon (years) 1 Average annual coupon rate for portfolio 2.09% Average beginning bond price for portfolio 101.01 Average ending bond price for portfolio (assuming roll-down and stable yield curve) 102.61 Expected effective duration for portfolio (at end of one year) 5.172 Expected convexity for portfolio (at end of one year) 0.799 Expected change in government bond yield curve –0.25%

**Q.** Based on the information provided in Exhibit 3, the expected return for Portfolio C is *closest to*:

- 4.70%.
- 3.65%.
- 4.95%.

Solution

**C is correct.** The correct answer is 4.95%. Calculations are shown in the table below.

Yield income 2.07% Roll-down return 1.58% Total rolling yield 3.65% Expected price change based on yield view 1.29% Total expected return 4.95%

Yield income = 2.09/101.01 = 2.07%.

Roll-down return = 102.61/101.01 − 1 = 1.58%.

Total rolling yield = 2.07 + 1.58 = 3.65%.

Expected price change based on yield view = (−MD × ΔYield) + [½ × Convexity × (ΔYield)^{2}] = (−5.172 × –0.0025) + [0.5 × 0.799 × (−0.0025)^{2}] = 1.29%.

Total expected return = 3.65% + 1.29% = 4.95%.